Answer:
The length and width of the patio are 18¹/₃ feet and 6²/₃ feet respectively.
Step-by-step explanation:
Let L and W be the length and width of the patio respectively. Since the patio is a rectangle, its perimeter, P = 2(L + W). This perimeter equals the length of string of lights which is 45 ft.
Now, the length of his patio, the side along the house, is five feet longer than twice its width implies that L = 2W + 5.
Substituting L into P, we have
P = 2(L + W)
= 2(2W + 5 + W)
= 2(3W + 5)
= 6W + 5
Since P = 45 feet,
6W + 5 = 45
6W = 45 - 5
6W = 40
W = 40/6
W = 20/3 feet
W = 6²/₃ feet
Since L = 2W + 5, substituting W = 20/3 into L, we have
L = 2W + 5
= 2(20/3) + 5
= 40/3 + 5
taking the L.C.M, we have
= (40 + 15)/3
= 55/3 feet
= 18¹/₃ feet
So, the length and width of the patio are 18¹/₃ feet and 6²/₃ feet respectively.
